3(x-7)(2x-4)=0

Solution for 3(x-7)(2x-4)=0 equation:

Simplifying
3(x + -7)(2x + -4) = 0

Reorder the terms:
3(-7 + x)(2x + -4) = 0

Reorder the terms:
3(-7 + x)(-4 + 2x) = 0

Multiply (-7 + x) * (-4 + 2x)
3(-7(-4 + 2x) + x(-4 + 2x)) = 0
3((-4 * -7 + 2x * -7) + x(-4 + 2x)) = 0
3((28 + -14x) + x(-4 + 2x)) = 0
3(28 + -14x + (-4 * x + 2x * x)) = 0
3(28 + -14x + (-4x + 2x2)) = 0

Combine like terms: -14x + -4x = -18x
3(28 + -18x + 2x2) = 0
(28 * 3 + -18x * 3 + 2x2 * 3) = 0
(84 + -54x + 6x2) = 0

Solving
84 + -54x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(14 + -9x + x2) = 0

Factor a trinomial.
6((2 + -1x)(7 + -1x)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {2, 7}